Gowdy cosmology and two-dimensional gravity

We obtain the Gowdy cosmology by compactifying (3+1)-dimensional general relativity on a two-torus {ital T}{sup 2}. We fix the conformal gauge in the resulting effective (1+1)-dimensional theory and show that it is equivalent to a nonlinear {sigma} model with a background minisuperspace metric and a background minisuperspace dilaton field. We generalize the Gowdy model by introducing a nonzero cosmological constant and nonzero {theta} angle and show that it is equivalent to a nonlinear {sigma} model with a background minisuperspace tachyon field and a background minisuperspace antisymmetric tensor field, respectively. The minisuperspace backgrounds do not lead to vanishing {beta} functions; in some cases, however, it is possible to shift the minisuperspace dilaton field to obtain vanishing {beta} functions in a manner similar to that of the Liouville model.